1. Field of the Invention
This invention relates to an apparatus for and a method of calculating a sum of products.
2. Description of the Related Art
In a digital filter of, for example, order p, products of p input data and p predetermined coefficients are successively added cumulatively. In other words, a sum of products of the p data and the p predetermined coefficients is calculated so that a desired filter output is outputted from the digital filter of order p.
In a conventional digital filter, when coefficients for calculation of a sum of products of data are processed in a fixed-point form, the accuracy of the coefficients is limited by a word length (bit number) handled in the apparatus. Accordingly, there is a subject that a round-off error takes place and consequently a desired filter output cannot be obtained.
It is one of possible solutions to the subject to increase the number of bits Which can be handled by the apparatus in order to reduce round-off errors. However, the solution still has a subject that the number of elements constituting the apparatus is increased and the power dissipation of the apparatus is increased.
Further, in a digital filter designed, for example, as a low-pass filter, since the absolute values of coefficients which are symmetrical with respect to a coefficient of order 0 generally decrease as the order number increases, when the number of bits which can be handled by the apparatus is increased, high order bits are not used with those coefficients which are high in order number, that is, those coefficients which are small in absolute value. Accordingly, the efficiency is low.
There is a method wherein coefficients are handled separately for an exponent part and a mantissa part, that is, in the floating point form. However, when products (products of data and coefficient) having comparatively small exponent parts are to be added cumulatively to products having comparatively large exponent parts, since the method truncates low bits of mantissa parts of the products having comparatively small exponent parts in order to make the sizes of the exponent parts of all of the products equal to one another, that is, to adjust the number of columns, it has a subject that it involves a number of round-off errors.